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The Advantages of Using Group Means in Estimating the Lorenz Curve and Gini Index From Grouped Data

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  • Merritt Lyon
  • Li C. Cheung
  • Joseph L. Gastwirth

Abstract

A recent article proposed a histogram-based method for estimating the Lorenz curve and Gini index from grouped data that did not use the group means reported by government agencies. When comparing their method to one based on group means, the authors assume a uniform density in each grouping interval, which leads to an overestimate of the overall average income. After reviewing the additional information in the group means, it will be shown that as the number of groups increases, the bounds on the Gini index obtained from the group means become narrower. This is not necessarily true for the histogram method. Two simple interpolation methods using the group means are described and the accuracy of the estimated Gini index they yield and the histogram-based one are compared to the published Gini index for the 1967--2013 period. The average absolute errors of the estimated Gini index obtained from the two methods using group means are noticeably less than that of the histogram-based method. Supplementary materials for this article are available online.[Received August 2014. Revised September 2015.]

Suggested Citation

  • Merritt Lyon & Li C. Cheung & Joseph L. Gastwirth, 2016. "The Advantages of Using Group Means in Estimating the Lorenz Curve and Gini Index From Grouped Data," The American Statistician, Taylor & Francis Journals, vol. 70(1), pages 25-32, February.
    • Handle: RePEc:taf:amstat:v:70:y:2016:i:1:p:25-32
    DOI: 10.1080/00031305.2015.1105152
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    Cited by:

    1. Kangmennaang, Joseph & Elliott, Susan J., 2018. "Towards an integrated framework for understanding the links between inequalities and wellbeing of places in low and middle income countries," Social Science & Medicine, Elsevier, vol. 213(C), pages 45-53.
    2. Yue Liu & Yuwei Su & Xiaoyu Li, 2022. "Analyzing the Spatial Equity of Walking-Based Chronic Disease Pharmacies: A Case Study in Wuhan, China," IJERPH, MDPI, vol. 20(1), pages 1-14, December.
    3. Joseph Chukwudi Odionye & Ethelbert Ukachukwu Ojiaku & Ndubuisi Agoh & Chikeziem F. Okorontah & Roy M. Okpara & Callistus Ogu, 2024. "Economic policy uncertainty and equity index in sub-Saharan African (SSA) countries: accounting for multiple structural breaks in a panel framework," SN Business & Economics, Springer, vol. 4(6), pages 1-30, June.
    4. Tatjana Miljkovic & Ying-Ju Chen, 2021. "A new computational approach for estimation of the Gini index based on grouped data," Computational Statistics, Springer, vol. 36(3), pages 2289-2311, September.
    5. Dilanka S. Dedduwakumara & Luke A. Prendergast & Robert G. Staudte, 2021. "Some confidence intervals and insights for the proportion below the relative poverty line," SN Business & Economics, Springer, vol. 1(10), pages 1-22, October.
    6. Youri Davydov & Francesca Greselin, 2020. "Comparisons Between Poorest and Richest to Measure Inequality," Sociological Methods & Research, , vol. 49(2), pages 526-561, May.
    7. Songpu Shang & Songhao Shang, 2021. "Estimating Gini Coefficient from Grouped Data Based on Shape-Preserving Cubic Hermite Interpolation of Lorenz Curve," Mathematics, MDPI, vol. 9(20), pages 1-11, October.

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